# qmvnorm: Quantiles of the Multivariate Normal Distribution In mvtnorm: Multivariate Normal and t Distributions

## Description

Computes the equicoordinate quantile function of the multivariate normal distribution for arbitrary correlation matrices based on inversion of `pmvnorm`.

## Usage

 ```1 2 3 4``` ```qmvnorm(p, interval = NULL, tail = c("lower.tail", "upper.tail", "both.tails"), mean = 0, corr = NULL, sigma = NULL, algorithm = GenzBretz(), ptol = 0.001, maxiter = 500, trace = FALSE, ...) ```

## Arguments

 `p` probability. `interval` optional, a vector containing the end-points of the interval to be searched. Does not need to contain the true quantile, just used as starting values by the root-finder. If equal to NULL a guess is used. `tail` specifies which quantiles should be computed. `lower.tail` gives the quantile x for which P[X ≤ x] = p, `upper.tail` gives x with P[X > x] = p and `both.tails` leads to x with P[-x ≤ X ≤ x] = p. `mean` the mean vector of length n. `corr` the correlation matrix of dimension n. `sigma` the covariance matrix of dimension n. Either `corr` or `sigma` can be specified. If `sigma` is given, the problem is standardized. If neither `corr` nor `sigma` is given, the identity matrix is used for `sigma`. `algorithm` an object of class `GenzBretz`, `Miwa` or `TVPACK` specifying both the algorithm to be used as well as the associated hyper parameters. `ptol, maxiter, trace` Parameters passed to the stochastic root-finding algorithm. Iteration stops when the 95% confidence interval for the predicted quantile is inside [p-ptol, p+ptol]. `maxiter` is the maximum number of iterations for the root finding algorithm. `trace` prints the iterations of the root finder. `...` additional parameters to be passed to `GenzBretz`.

## Details

Only equicoordinate quantiles are computed, i.e., the quantiles in each dimension coincide. The result is seed dependend.

## Value

A list with two components: `quantile` and `f.quantile` give the location of the quantile and the difference between the distribution function evaluated at the quantile and `p`.

`pmvnorm`, `qmvt`

## Examples

 `1` ```qmvnorm(0.95, sigma = diag(2), tail = "both") ```

### Example output

```\$quantile
[1] 2.236422

\$f.quantile
[1] -1.310417e-06

attr(,"message")
[1] "Normal Completion"
```

mvtnorm documentation built on Jan. 26, 2018, 3:03 a.m.